Thanks for the review, I appreciate it. Of course, I do not agree with all your comments and I’ve posted a response here:

https://measuringstatisticalevidence.wordpress.com/

These matters need lots of discussion.

Mike

]]>> avoid the selection of a “nice” version of the density.

Are you agreeing or disagreeing with Evans derivations from Rudin?

> for Murray Aitkin to introduce his integrated likelihood paradigm

Aitkin uses profile likelihood for marginalization (i.e. H-likelihood) so it is different.

> another type of MAP then

It is not a MAP and has different properties e.g. invariance to reparameterizations.

> burdened with a number of arbitrary choices, lacking the unitarian feeling associated with a regular Bayesian decisional approach

OK, but Evans specifically avoids loss functions and decision theory stating that they can’t be empirical checked – “given the need of empirically checking every aspect of those analyses”. I don’t think he would object to subsequently choosing a loss function.

It is a long book with I believe much depth, but I am biased and perhaps should end with an encouragement for editing for further clarity of your position.

Keith O’Rourke

p.s. Thanks.

http://www.bayesianphilosophy.com/the-data-can-change-the-prior/

All of that is instantly Bayesian since it’s derived from the sum/product rules like Bayes Theorem. Anyone who objects to it for any reason is violating the most basic, widely accepted, and widely used equations in probability theory.

What more needs to be said?

]]>I knew nothing about Evans book apart from something commented here on the ‘Og, and for that I’m very grateful.

So far, however, what has really interested me in the idea of taking ratios of probabilities w.r.t. the prior is that it is an operation similar to taking ratios of an index of the information content of the probability densities. In particular, I keep wanting to take the log of such a ratio and try to relate it to relative information or to some information criterion. After all, the prior could be accepted as a model of the parameter space which ignores data. A good model will be better than the prior. A bad model won’t. One reason, in my view, why Uniform priors are unhelpful is that they are maximally uninformative.

Anyway, I need to work through the book and then see if there’s any mathematical flesh on these thin bones.

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